Richardson has 43 goals and 62 assists in 391 career games with Colorado and Los Angeles. He was a member of the Kings' Stanley Cup-winning team in the 2011-12 season.
He had a goal and five assists on 16 games for the Kings last season.
Richardson welcomed the chance to play in Vancouver after a season in which he found himself at times a healthy scratch in Los Angeles.
"To be honest I was super-frustrated," he told a media conference call. "It was really tough. They didn't give me a whole lot of feedback on why I wasn't playing either which was tough.
"At the end of the year, it turned around. I got in there and started playing and played well."
He has played all three forwards positions but says the Canucks want him to play his preferred centre role.
"They made me feel like they really wanted me," he said of the Canucks.
Richardson, who expects to play on Vancouver's third line, says his experience playing against the Canucks in the playoffs had shown him he was joining a tough team to play against.
"Great goaltending, great forwards, great D. They've got everything," he said.
Weber spent the last five seasons with the Montreal Canadiens organization. The Swiss blue-liner has five goals and 27 assists in 115 games with the Habs.
He had two assists in six games last season.